Is converting Fixed Pt. (fixed n bit for fraction) to IEEE double safe ?
ie: does IEEE double format can represent all numbers a fixed point can represent ?
The test: a number goes to floating pt format then back to it's original fixed pt format.
Assuming your fixed point numbers are stored as 32-bit integers, yes, IEEE double precision can represent any value representable in fixed point. This is because double has a 53-bit mantissa, your fixed point values only have 32 bits of precision, and the floating-point exponent for the fixed point value is bounded between -32 and 32 (depending on where you consider the binary-point to lie in your fixed point values) which is well within the representable range.